In Super Mario 64, the Game Over animation starts with Mario’s head flying towards the screen. During the first few frames of this animation, while it is far from the camera, the head does not render correctly. Here it is zoomed in.
In the newer Super Mario series games starting with the Wii U, Princess Daisy’s nose has no texture. It is entirely modeled in polygons and becomes indistinguishable when lit from the front. By contrast, Princess Peach’s nose is still textured.